Maybe the game is figuring out HOW to send him messages and assistance. Like the princess is trapped in a room full of stuff and she has to figure out that she has to grab a tapestry off the wall and charcoal ash from the fireplace so she can write a big message on the tapestry saying ""I'M IN HERE" and then hang it out the window so the knight can find which room she's in.

And another puzzle could be that she has to figure out how to get a key to the knight who is unable to get past a locked gate in a hallway, so the princess has to find the key, and then she has to figure out that she has to tie it to the waist of a guard who walks around the hallways so that the knight can grab the key off the guard.

Another puzzle could be something with figuring out you have to do something with a rat that scurries between areas.

Another could be doing something with a bird that flies somewhere and does something helpful

Another could be using the toilet tube to drop out a map to the knight waiting below (castle toilets were just a hole in the wall)

Another could be freeing a monster from another cell so the monster will kill all the warriors waiting in the hallway before the knights arrival

Another could be talking to the person who delivers her meals to convince/trick him into doing something outside like drawing an arrow on a hallway wall so the knight knows which way he should go

Etc.

And importantly you can have the story lead to her being in different locations so that the game environment can change to keep it fresh. Like as the knight starts to get close to her location the bad guys will move the princess to a more secure cell (with a wink message to the player audience referencing mario "the princess is in another castle"). And the game can actually start with her trapped in a wing of her home castle with her dad (the king) trying to keep her chaste away from interaction with any men. So she can be trapped in multiple different places throughout the game as the player advances through the game